The invention relates to the field of cellular solids as well as heterogeneous or filled materials, and in particular to materials possessing a periodic structure that experiences a transformation in the structural configuration upon application of a critical macroscopic stress or strain.
There are many examples of cellular solids in nature and they are mimicked in numerous synthetic materials ranging from heterogeneous foams to engineered honeycombs. These cellular structures are used in a wide variety of mechanical, acoustic and thermal applications. The connections between the microstructure of such materials and their macroscopic properties have been investigated by many researchers. Research into the mechanics and structural properties of cellular solids can be categorized according to the designed role of the material: high stiffness to weight; high strength to weight; or low density, high energy absorption materials. Energy absorption is achieved by capitalizing on the large deformations and collapse of the cellular structures when deformed beyond the initial linear elastic regime.
The nonlinear stress-strain behavior of foams which possess a heterogeneous cell structure and honeycombs which possess a periodic structure have been of particular interest. Under compression, the transition from linear elastic behavior to either a “yield” or plateau stress (or, in some instances, a “yield” with some subsequent strain hardening) has been found to result from an initial instability. This usually originates in the buckling of a member or a wall in the cell microstructure which then leads to localized deformation into bands. The collapse bands can progress through the structure at relatively constant stress. This energy absorbing, collapse behavior has been clearly demonstrated in experimental and modeling studies of a wide range of two-dimensional honeycomb structures including hexagonal and circular structures with different wall dimensions and elastic-plastic mechanical behavior. The two-dimensional periodic honeycomb structures have enabled investigators to vary different parameters in a controlled manner to study the effect of geometric features and imperfections on the onset of the instability and its subsequent localization into deformation bands.
As discussed above, cellular structures provide unique energy absorption opportunities through their nonlinear stress-strain behavior—particularly through the ability to undergo very large deformation at constant or near constant stress once localization takes place. While this mechanical function of cellular solids is of great importance, it should also be recognized that periodic structures also provide many other functions and/or attributes in natural materials. Studies on butterflies, beetles, moths, birds and fish have shown that the iridescent phenomena are related to the presence of surface and/or subsurface photonic crystal microstructures. Photonic crystals are composed of submicron structures with periodicity comparable to the wavelength of visible light which are designed to affect the propagation of electromagnetic waves. Therefore, they are attractive optical materials for controlling and manipulating light with applications including LEDs, optical fibers, nanoscopic lasers, ultrawhite pigment, radio frequency antennas and reflectors, and photonic integrated circuits. In a similar way, photonic crystals are periodic composite materials with lattice spacings comparable to the acoustic wavelength. They are of interest because of the profound effects of their periodic structure on wave propagation (e.g., the existence of acoustic band gaps), and because of potential applications as sound filters, transducer design and acoustic mirrors. Periodic submicron structures are also employed to obtain super-hydrophobicity. Micro-textures that modify the wettability of the material have been found in the leaves of about 200 plants, including asphodelus, drosera, eucalyptus, euphorbia, gingko biloba, iris, lotus and tulipa, as well as in butterfly wings, duck feathers, bugs and desert beetles.
Recently, the ability to synthetically produce periodic structures at the micron and submicron length-scales through microfabrication, interference lithography, as well as thermodynamically-driven self-assembly has created new opportunities to mimic natural structures and properties. These periodic structures are generally static or, in some instances, change in a more or less affine nature with deformation or other external stimuli. Hence, properties which are dependent on the precise length scale and/or spacing of the periodic features will exhibit a gradual monotonic change with deformation.